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Proof step 38 from proof getShort-isi (previous step)

0 ≤ b2i(byi) ⊦ s2i(i2s(bor(256 * bits2uint(int2bits(b2i(byi))), band(b2i(byj), 255)))) = bor(256 * bits2uint(int2bits(b2i(byi))), band(b2i(byj), 255)), ¬ bor(256 * bits2uint(int2bits(b2i(byi))), band(b2i(byj), 255)) < ~32768 ∧ ¬ 32767 < bor(256 * bits2uint(int2bits(b2i(byi))), band(b2i(byj), 255))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
⊦ 0 ≤ i → int2bits(i) = uint2bits(i)
Proof step 40:
0 ≤ b2i(byi), 0 ≤ b2i(byi) ⊦ s2i(i2s(bor(256 * bits2uint(uint2bits(b2i(byi))), band(b2i(byj), 255)))) = bor(256 * bits2uint(uint2bits(b2i(byi))), band(b2i(byj), 255)), ¬ bor(256 * bits2uint(uint2bits(b2i(byi))), band(b2i(byj), 255)) < ~32768 ∧ ¬ 32767 < bor(256 * bits2uint(uint2bits(b2i(byi))), band(b2i(byj), 255))

Rule argument

seq: ⊦ 0 ≤ i → int2bits(i) = uint2bits(i) subst: [i] → [b2i(byi)] rotate: F spec: int2bits inst: name: int2bits-pos

Additional information

Used terms: b2i(byi)